I can’t think of any normal scenario the 604 would need 2 stops between Nice and US west coast. In early 2000s I operated a CL 604 many times between US West coast (KOAK specifically), to Nice and never had to make more than 1 stop either way. We wouldn’t fly NAT....went random route. CYFB is midway on great circle and a typical tech stop but there are plenty of other good options.
Last time I looked CL 604 has a 3700nm range?
Maybe your advisor was thinking CL 601 when he said 2 stops westbound would be needed? Even then a 601 would be able to do it with 1 stop westbound.